\(\frac{1}{2}x+\frac{4}{5}\cdot\left(2\frac{1}{2}+x\right)=3\frac{3}{4}\)
\(\frac{1}{2}x+\frac{4}{5}\cdot\left(\frac{5}{2}+x\right)=\frac{15}{4}\)
\(\frac{1}{2}x+\frac{4}{5}\cdot\frac{5}{2}+\frac{4}{5}\cdot x=\frac{15}{4}\)
\(\frac{1}{2}x+2+\frac{4}{5}x=\frac{15}{4}\)
\(\frac{1}{2}x+\frac{4}{5}x=\frac{15}{4}-2\)
\(\frac{1}{2}x+\frac{4}{5}x=\frac{7}{4}\)
\(x\left(\frac{1}{2}+\frac{4}{5}\right)=\frac{7}{4}\)
\(x\cdot\frac{13}{10}=\frac{7}{4}\)
\(x=\frac{7}{4}:\frac{13}{10}\)
\(x=\frac{35}{26}\)
\(\frac{1}{2}x+\frac{4}{5}\cdot\left(2\frac{1}{2}+x\right)=3\frac{3}{4}\)
\(\frac{1}{2}x+\frac{4}{5}\cdot\left(\frac{5}{2}+x\right)=\frac{15}{4}\)
\(\frac{1}{2}x+\frac{4}{5}\cdot\frac{5}{2}+\frac{4}{5}\cdot x=\frac{15}{4}\)
\(\frac{1}{2}x+2+\frac{4}{5}x=\frac{15}{4}\)
\(\frac{1}{2}x+\frac{4}{5}x=\frac{15}{4}-2\)
\(\frac{1}{2}x+\frac{4}{5}x=\frac{7}{4}\)
\(x\cdot\left(\frac{1}{2}+\frac{4}{5}\right)=\frac{7}{4}\)
\(x\cdot\frac{13}{10}=\frac{7}{4}\)
\(x=\frac{7}{4}-\frac{13}{10}\)
\(x=\frac{9}{20}\)